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2007

Graph classes with given 3-connected components: asymptotic counting and critical phenomena

13 years 11 months ago
Graph classes with given 3-connected components: asymptotic counting and critical phenomena
Fix a family T of 3-connected graphs, and let G be the class of graphs whose 3connected components are the graphs in T . We present a general framework for analyzing such graph classes based on singularity analysis of generating functions. This generalizes previously studied cases such as planar graphs and series-parallel graphs. We provide a general theorem for the asymptotic number of graphs in G, based on the singularities of the exponential generating function associated to T . For some of the classes under study we show the presence of critical phenomena as the edge density in the class varies.
Omer Giménez, Marc Noy, Juan José Ru
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2007
Where ENDM
Authors Omer Giménez, Marc Noy, Juan José Rué
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